A 1.20 kg rock is placed on a vertical spring of negligible mass and force constant k=1800 n/m that is compressed 15.0 cm. when the spring is released, how high does the rock rise from this initial position?

1.95 m

Explanation: according to the law of conservation of energy, the elastic potentials energy in the spring is responsible for the movement of the stone vertically.

Elastic potential energy = potential energy

Elastic potentials energy = 1/2kx²

Where k = spring constant = 1800 N/m

x = compression = 15cm = 0.15m

Potential energy = mgh

Where m = mass of rock = 1.2 kg

g = acceleration due to gravity = 9.8m/s²

h = height =?

1/2kx² = mgh

kx² = 2mgh

1800 × (0.15)² = 2(1.2 × 9.8 × h)

1800 × 0.0225 = 2.4 × 9.8 × h

h = 1800 × 0.0225/ 2.4 × 9.8

h = 45.9/ 23.52

h = 1.95 m

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